Dynamics of imitation

In the model, each person in a large population chooses between two options , such as adhering to or not adhering to a social norm. People observe each others' choices at random and adjust their adherence probabilities in imit ative directions. It is known from earlier work that, under strong restrict ions on the imitation, the distribution of adherence probabilities will eit her evolve upward toward a high adherence equilibrium or downward toward a low adherence equilibrium, depending on initial conditions. The intuition i s that imitation leads to uniformity; Here we show that more general forms of imitation allow a much wider variety of outcomes. There can be a sizable number of equilibria and a variety of stability patterns. In mathematical form, the model is an interactive Markov chain.